Approximation properties of haplotype tagging

BACKGROUND: Single nucleotide polymorphisms (SNPs) are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. RESULTS: It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n(2 )- n)/2) for n haplotypes but not approximable within (1 - ε) ln(n/2) for any ε > 0 unless NP ⊂ DTIME(n(log log n)). A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O([Image: see text] (2m - p + 1)) ≤ O(m(n(2 )- n)/2) where p ≤ min(n, m) for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. CONCLUSION: The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel

Extracting large quasi-bicliques using a skeleton-based heuristic

One important computational problem is that of mining quasi bicliques from bipartite graphs. It is important because it has an almost endless number of applications and, in most real world problems, is more appropriate than the mining of bicliques. In my thesis I examine the following: the motivation for quasi bicliques, the existing literature for quasi bicliques, my implementation of a web application that allows the user to compute exact quasi biclique solutions using the biclique formulation and the exact solution algorithm provided by Chang et al.[1], and finally a polynomial heuristic algorithm for finding large quasi bicliques in the special case where we have all the biclique subgraphs of a bipartite graph available

Primal-dual heuristics for solving the set covering problem

The set covering problem (SCP) is a well known combinatorial optimization problem applied widely in areas such as; scheduling, manufacturing, service planning, network optimization, telecommunications, and so on. It has been already shown that SCP is NP-hard in the strong sense [15]. Therefore, many heuristic and enumerative algorithms have been developed to solve SCP effectively. The primary purpose of the present study is to develop an effective heuristic for SCP. The heuristic is based on a primal-dual approach which is commonly used in the literature for approximating NP-hard optimization problems. In this study, we present numerical results to evaluate the performance of the heuristic as well as our observations throughout the development process. Our results indicate that the heuristic is able to produce good results in terms of both solution quality and computation time. Moreover, we show that the proposed heuristic is simple, easy to implement and has a potential to solve large-scale SCPs efficiently

Heuristic algorithms for wireless mesh network planning

x, 131 leaves : ill. ; 29 cmTechnologies like IEEE 802.16j wireless mesh networks are drawing increasing attention of the research community. Mesh networks are economically viable and may extend services such as Internet to remote locations. This thesis takes interest into a planning problem in IEEE 802.16j networks, where we need to establish minimum cost relay and base stations to cover the bandwidth demand of wireless clients. A special feature of this planning problem is that any node in this network can send data to at most one node towards the next hop, thus traffic flow is unsplittable from source to destination. We study different integer programming formulations of the problem. We propose four types of heuristic algorithms that uses greedy, local search, variable neighborhood search and Lagrangian relaxation based approaches for the problem. We evaluate the algorithms on database of network instances of 500-5000 nodes, some of which are randomly generated network instances, while other network instances are generated over geometric distribution. Our experiments show that the proposed algorithms produce satisfactory result compared to benchmarks produced by generalized optimization problem solver software